Share Buyback and Equity Issue Anomalies Revisited

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1 Share Buyback and Equity Issue Anomalies Revisited Theodoros Evgeniou, Enric Junqué de Fortuny, Nick Nassuphis, and Theo Vermaelen February 4, 2016 Abstract We re-examine the behavior of stock returns after share buyback and equity issuance announcements using the five-factor model proposed by Fama and French (2015a). We confirm the findings of Fama and French (2015b) that the equity issue anomaly, i.e., the fact that equity issues are followed by negative long-term excess returns, disappears after replacing the Fama and French (1993) three-factor model with the five-factor model. However, long term positive excess returns after buyback announcements, first reported by Ikenberry, Lakonishok, and Vermaelen (1995), remain economically and statistically significant. Moreover, the Undervaluation Index proposed by Peyer and Vermaelen (2009) remains a useful proxy for the likelihood that the buyback is driven by undervaluation. The buyback anomaly is robust over time and across sectors. Firms with low correlations with the market seem to be better at market timing, which is consistent with the hypothesis that the repurchase is driven by superior companyspecific information. Firms with high pre-announce stock returns volatility also have higher abnormal returns, which is consistent with the hypothesis that a repurchase authorization is an option to take advantage of undervaluation as argued by Ikenberry and Vermaelen (1996). This result is also consistent with Stambaugh, Yu, and Yuan (2015) who find a positive relation between stock returns and idiosyncratic volatility for undervalued stocks, and unlike the well-known low volatility anomaly. Finally, based on these findings, we develop an enhanced Undervaluation Index that improves abnormal returns relative to the index developed by Peyer and Vermaelen (2009). JEL classification: G35 Keywords: Share Buybacks, Seasoned Equity Offerings INSEAD, Bd de Constance, Fontainebleau, France, phone: +33(0) , 31, St. Martin s Lane WC2N 4ER London, United Kingdom, theodoros.evgeniou@insead.edu, enric.junquedefortuny@insead.edu, nicknassuphis@gmail.com, and theo.vermaelen@insead.edu.

2 1. Introduction The fact that companies experience long-term positive excess returns after share buybacks and negative long term excess returns after equity issues, has been documented extensively in the academic literature. 1 In spite of these well documented anomalies investors are not less excited today about e.g., a buyback announcement than 30 years ago: on average stock prices increase by approximately 2 to 3% when companies announce that the board of directors has approved a buyback program. Moreover, we find very few funds that specialize in exploiting these anomalies. 2 The fact that these anomalies have not generated a significant response from investors and asset management firms is somewhat surprising considering that other anomalies have disappeared after being documented in academic research (Engelberg, McLean, and Pontiff, 2015). What makes these capital structure anomalies different so that they stand the test of time? One straightforward explanation is that they are not really anomalous returns but compensation for risk. Excess returns in previous research are calculated using the Fama and French (1993) three-factor model or the Carhart (1997) 4-factor model as benchmarks. However, Fama and French (2015b) argue that the buyback and equity issue anomalies do not survive after using the more recent Fama and French (2015a) five-factor asset pricing model as a model of expected returns. This model incorporates new evidence that profitability and investment patterns, besides market to book and size, explain stock returns (Novy-Marx (2013)). If buybacks (equity issues) are done by firms with high (low) profitability and few (many) investment opportunities, then these factors may well explain the excess returns re- 1 For evidence on long-term excess returns after buybacks see e.g., Ikenberry et al. (1995); Peyer and Vermaelen (2009); Manconi, Peyer, and Vermaelen (2015). For evidence on under-performance after equity issues see e.g., Loughran and Ritter (1995); Spiess and Affleck-Graves (1995); Eckbo, Masulis, and Norli (2000); Dittmar and Thakor (2007); Brav, Geczy, and Gompers (2000). 2 For example, a Google search for buyback funds gives very few results: Powershare Buyback Achievers fund, KBC Buyback America, S&P 500 Buyback ETF, Catalyst/Equity Compass Buyback Strategy fund, and PV Buyback USA. The first 3 funds focus on large caps after buyback completions although the academic research shows abnormal returns are more significant in small, under-priced, value stocks and the relevant event is not the completion of the buyback but the buyback authorization. We are also not aware of eventdriven hedge funds that buy repurchasing firms and short equity issuers; typical event-driven strategies are for example based on M&A arbitrage, capital structure arbitrage or on investing in distressed securities. 1

3 ported in previous research. Note, however, that Fama and French (2015b) do not exactly replicate the papers that first reported the anomalies. First, they assume investors buy after the completion of the buyback and the equity issue, not around the announcement date as e.g., Peyer and Vermaelen (2009). For buybacks this may be an issue as repurchases may be completed several years after the buyback authorization (Stephens and Weisbach (1998)). Moreover Fama and French (2015b) do not examine repurchases and equity issues separately: they calculate returns after net equity issues (funds spent on buybacks minus funds spent on equity issues). The part of their sample where net equity issues are positive is defined as the buyback sample. But this sample still contains some equity issuers, which may introduce a downward bias in the excess returns calculations. Moreover the idea of pooling buybacks and equity issues in net issues assumes that the decision to issue equity is simply the mirror of buying back shares. However, issuing stock to new investors is not the same as buying back stock from old selling investors. In the first case, the management has to face new shareholders that may face potential losses, while in the second case the firm only takes advantage of selling shareholders who leave the firm. In this paper we re-examine the anomaly using the Fama and French (2015a) model but use announcement dates and separate buyback announcements and equity announcements. A second possible reason for the funds lack of interest in the buyback anomaly is that event studies aggregate returns over a very long horizon. The fact that buying shares after a buyback announcement generates positive excess returns during for example does not mean that, if one starts a fund in 2016, one can expect to beat the market during the next 3 years. In other words, the anomaly may be time dependent, and investor patience may not extend beyond 3 years. Moreover, because of the growth of institutional investors and the reduction in trading costs markets may have become more efficient in recent years as argued by Fu and Huang (2015). The anomaly may also be industry-specific so that an investor who follows a buyback strategy may end up with a highly undiversified portfolio. The long-term event studies also do not give much guidance about when to sell after a 2

4 buyback or cover after shorting an equity issue. Trading strategies, such as M&A arbitrage (Mitchell and Pulvino (2001)), often have natural exit decision points (e.g., at M&A deal completion or termination), but the literature does not provide clear guidance about when to exit a buyback position. Empirical studies tend to show that, on average, excess returns continue for up to 3 or 4 years after a buyback authorization, but there is no reason why such a horizon is optimal. One straightforward early selling strategy that we study is to combine the buyback and equity issuance anomalies by selling buyback stocks after the firm announces an equity issue. Note that the fact that equity issues in general are followed by negative abnormal returns does not necessarily imply that equity issues after buybacks should generate the same result. Finally, the results from event studies which use either Ibbotson RATS or the Calendar Time method estimate excess returns and risks jointly. Investors, such as hedge funds, who would like to exploit the anomaly and hedge market risk need however to estimate the factor betas using historical information. If the buyback signals a change in risk (as argued by Grullon and Michaely (2004)) hedging market risk may be complicated. That is why in this paper we also simulate hedged investment strategies where we estimate risk before forming the portfolios. The purpose of this paper is to explore these concerns by studying the robustness of the buybacks and issuance anomalies over the 30 year period starting in January 1985 and ending in December 2014, using the Fama and French (2015a) five-factor model. Although there are other models of market equilibrium proposed to explain excess returns after buyback authorizations (i.e. Lin, Stephens, and Wu (2014)) our focus is on the Fama and French (2015a) challenge. We confirm the Fama and French (2015b) conclusion that the five-factor model makes the equity issue anomaly disappear, but the buyback anomaly remains statistically and economically significant. Even though we find that equity issues are not followed by significant negative excess returns in general, it turns out that using a SEO announcement as a sell signal improves the performance of a buyback portfolio. The interpretation is that firms that are timing the market by buying back shares when they are cheap are also success- 3

5 ful timing the market when stocks are expensive. We also confirm that the Undervaluation Index developed by Peyer and Vermaelen (2009) is a good predictor of excess returns and that the anomaly does not disappear if we exclude specific industries, although that Index is mostly relevant for smaller firms. We also test whether the buyback anomaly is related to the even better known low volatility anomaly: that (idiosyncratic) volatility is negatively related to future returns. For example, Ang, Hodrick, Xing, and Zhang (2006) find negative alphas for high volatility and high idiosyncratic volatility stocks, using the 3 factor Fama and French (1993) model. Moreover, Fama and French (2015b) show that, using the 5 factor model, this anomaly persists for small firms. However, in our buyback sample we find a significant positive relation between excess returns, using the the Fama-French 5-factor model as a benchmark. This is consistent with the information advantage hypothesis: in firms with high idiosyncratic risk volatility is largely driven by company-specific information, and in such firms it is more likely that management is better informed than the market. The result is also consistent with Stambaugh et al. (2015) who find a positive relation between stock returns and idiosyncratic volatility for undervalued 3 stocks. Turning to total volatility we also find that buyback authorizations of high risk stocks are followed by larger excess returns. This is consistent with the option hypothesis: a repurchase authorization is an option to take advantage of undervaluation and this option should be more valuable for high volatility stocks (Ikenberry and Vermaelen (1996)). If markets underestimate the value of this option at the time of the buyback authorization, excess returns should be positively correlated with volatility. Combining idiosyncratic risk and total volatility with the Peyer and Vermaelen (2009) Undervaluation Index into an Enhanced Undervaluation Index, improves the predictability of excess returns. In particular, during the four years following the buyback announcement, the high Enhanced Undervaluation Index portfolio generates an excess return of 0.82% per month with the Calendar Time event 3 They define undervaluation on the basis of a combination of 11 return anomalies reported in the literature, including net equity issuance. 4

6 study method. Using the IRATS method the cumulative excess return reaches 54.69% after 48 months. This paper is organized as follows. In section 2 we describe our data. In section 3 we test whether buyback and equity issue anomalies survive when we use the Fama and French (2015a) five-factor model. We also compare firms that buy back stock and issue equity within 48 months of a buyback announcement with firms that do not issue stock subsequently. In section 4 we test whether the buyback anomaly is robust across time, investment horizon and industry. In section 5 we test whether idiosyncratic risk as well as volatility can improve the predictability of excess returns, relative to simply using the Undervaluation Index proposed by Peyer and Vermaelen (2009). Section 6 concludes. 2. Data Our sample spans the period from January 1985 to December We start in 1985 as SDC s coverage is poor before that year. We stop in 2014, the last year all CRSP and Compustat data were available. We retrieved buyback authorization announcements and announcements of Secondary Equity Offerings (SEO s) from the Securities Data Corporation (SDC) database. Daily and monthly returns, pre-announcement daily closing prices and market capitalization data were taken from CRSP. Book value of equity (BE) was taken from Compustat. The Fama-French factors and breakpoints were obtained from Kenneth French s website. For the buybacks we combined all open market repurchase announcements from both the SDC Repurchases data base and the SDC US mergers and acquisitions (M&A) data base. 4 We ended up with a total of 24,190 repurchases events, out of which 12,030 were only from the SDC Repurchases database, 6,593 only from the SDC M&A database and 5,567 from both. Finally, we removed the following events: no CRSP returns available (5,287 events); 4 More information is available upon request. An interactive online tool to explore data variations and robustness analyses of all results in this paper is also available upon request. 5

7 not all Compustat data available (2,185 events); the percent of shares authorized was larger than 50% (63 events), or the closing price was less than $1 for events before 1995 or $3 for the other (713 events), or the primary stock exchange was not the NYSE, the Nasdaq, or Amex (1,586 events). Finally, we removed all events from firms in the Financial and Utilities sectors (3,594 events). 5 At the end we are left with 10,124 buyback events made by 3,661 firms. The average percent of share authorized for these firms was 7.3% (median of 5.8%), the average Market Capitalization at announcement was $6,039 Million (median of $806.9 Million), while the BE/ME was on average 0.6 (median of 0.4). For the issuers, we started with 12,265 events from SDC, filtered to exclude rights issues, pure secondary offerings where existing shareholders sell shares without generating proceeds for the company, issues made by non-u.s. firms or in non-u.s. markets, issues made by closedend funds or unit investment trusts, as well as block trades, accelerated offers and best efforts. We removed all SDC events for which either the event date (1,923 events) or the CUSIP (1,802 events) was missing or where we found duplicate events with mismatching information (40 events), a total of 3,402 events - given the overlap between these cases. Finally, as for the buybacks, we removed the following events: no CRSP returns available (1,982 events); not all Compustat data available (1,735 events); the percent of shares authorized was larger than 50% (44 events), or the closing price was less than $1 for events before 1995 or $3 for the other (278 events), or the stocks were not listed on the NYSE, Nasdaq or Amex (312 events). We again removed all events from firms in the Financial and Utilities sectors (476 events). Our final sample contains 3,250 issuers events made by 2,353 firms. The average percent of shares issued was 16.9% (median of 15.8%), the average Market Capitalization on the announcement day was $1,210 Million (median of $314.1 Million), while the BE/ME was on average 0.6 (median of 0.4). Figure 1 shows the number of announcements per year in the sample period as well as the 5 We are using the industries from Kenneth French s Website. The Financial Sector consists of all firms with SIC code at the time of the buyback announcement that belonged in the Banks or Fin industries (SIC codes 6000 to 6300 and 6700 to 6799). The Utilities Sector consists of all firms with SIC code 4900 to

8 (standardized) level of the S&P 500. Buyback activity rises prior to stock market increases and tends to fall afterwards, especially during the financial crisis of 2008 when buyback announcements fell to a 15 year low. Note the structural decline in equity issues since Share Buybacks, Equity Issues and Abnormal Returns We start with revisiting past research but now using a longer time period and the fivefactor model of Fama and French (2015a) to measure expected returns. In particular, we test whether buyback (equity issue) announcements are followed by significant positive (negative) long term excess returns, and if so, whether the returns can be explained by proxies for undervaluation as proposed by Peyer and Vermaelen (2009) Share buybacks and Equity Issues in Isolation Table 1, Panel A, shows long-term cumulative excess returns for various holding periods after the announcement using the Ibbotson RATS event study method. Each event month t we run cross-sectional regressions of stock returns against the factors. The intercept in the regression measures the average abnormal excess return in event month t. We then accumulate these excess returns over various time horizons (up to 48 months after the event). The advantage of this method is that each event gets the same weight and that factor betas are allowed to change in event time, something that may be important as capital structure changes may signal a change in risk (Grullon and Michaely, 2004). The table compares the excess returns using the Fama and French (1993) three-factor model and the Fama and French (2015a) five-factor model. The results show that, although using a fivefactor model lowers excess returns, the excess returns are statistically significantly positive over all investment horizons and reach 13.02% after 4 years (t=11.92). So the buyback anomaly does not disappear when we use a five-factor model. In all the tables we also 7

9 calculate cumulative excess returns in the 6 months prior to the buyback. Consistent with past research (e.g., Peyer and Vermaelen (2009)) buyback authorization announcements are preceded by significant negative excess returns of around -7%. This is consistent with the hypothesis that the typical repurchase announcement is triggered by at least the perception of insiders that the stock is undervalued. Table 2, Panel A, shows the results for all equity issues, using the same methodology as in Table 1, Panel A. Our results are largely consistent with Fama and French (2015b). Using the three-factor model, we find statistically significant long term (after 48 months) negative cumulative excess returns of -4.86% (t=-2). However, once we use the five-factor model as a benchmark, excess returns fall and become statistically insignificant after 48 months. This shows that when searching for anomalies, buybacks and equity issues should not be pooled in a net issue measure. Unlike buybacks, equity issues are firm commitments and announced and completed at the same point in time. Using actual shares issued (the measure used by Fama-French (1995b)) and equity announcements (our measure) should therefore produce similar results. Buyback authorization announcements on the other hand are not firm commitments and are often executed over a long period after the announcement. Actual repurchase dates thus do not correspond to announcement dates. Note also that equity issues are typically preceded by large positive excess returns of around 35% in the 6 months prior to the equity issue. However, the lack of post announcement negative excess returns shows that this was not reflecting irrational exuberance but rather that these firms experienced a substantial increase in growth opportunities and issued equity to finance them. One critique of the Ibbotson (1975) RATS method is that the result may be time-specific. Indeed as every event is equally weighted the cumulative average abnormal returns are dominated by periods when there are a large number of events. So we also use the Calendar Time method where in each calendar month we form an equally-weighted portfolio of all firms that announce a buyback (or an equity issue) in the previous t months. We then run a time series regression of the portfolio returns against the factors. The intercept of the regression is the average 8

10 monthly excess return in the t months after the event. The results in Panel B of Tables 1 and 2 are similar to Panel A of the same tables. Abnormal returns after buybacks are smaller when the five-factor model is used but remain statistically significant over all horizons. For example, over the 48 month horizon the average monthly excess return is 0.22% (t=2.95) which corresponds to 10.56% over 48 months. Note also that excess returns fall when the investment horizon increases. The largest monthly excess return (0.64%) is earned by the portfolio that holds buyback stocks for one month (not reported in Table 1) and the smallest excess return (0.22%) is earned by the portfolio that picks buybacks announced during the previous 48 months. This clearly shows that forming portfolios after buybacks are completed (as is done by measuring net issues in Fama and French (2015b)) is introducing a downward bias as many repurchase programs are completed several months (sometimes years) after the buyback announcement. Waiting until the buyback is completed means missing the largest excess returns earned shortly after the buyback authorization. Finally, there are no statistically significant excess returns after equity issues, regardless whether we use the three or five-factor model. Next we test whether the Undervaluation Index (U-index) developed by Peyer and Vermaelen (2009) using buyback announcements from 1991 to 2002 is a robust indicator to separate companies that are buying back stock because they are undervalued from companies that repurchase shares for other reasons. We calculate the U-index as follows. Companies get a size score from 1 (large firms) to 5 (small firms) depending on the quantile of their market value of equity in the month prior to the buyback announcement. Then, we calculate the 11-months pre-announcement absolute returns of months -12 to -1 before announcement for all events and assign a score of 5 to the low returns firms and 1 to the high returns ones. Finally, companies get a book value to market value (BE/ME) score depending on the quantile of their BE/ME value of equity in the year prior to the buyback announcement, with a score of 1 to small BE/ME firms and 5 to large ones. Unlike Peyer and Vermaelen (2009) who use all CRSP companies to define the quantile thresholds, we use the Fama- 9

11 French breakpoints for prior returns the month before, ME the month before, and BE/ME the year before the event to rank the firms from 1 to 5: for example, firms falling below the 5 th BE/ME breakpoint are assigned a score of 1, while companies above the 16 th BE/ME breakpoint are assigned a score of 5. We sum up these three scores for each firm and we then define as high U-index the firms with total score more than 11 and as low U-index those with total score less than 6. Note that unlike Peyer and Vermaelen (2009) we do not consider the stated reasons for the buyback in the press release, hence we define different thresholds for the high U-index and low U-index buyback firms. We end up with 2,955 high U-index buyback stocks (29.19% of all buyback events), and 2,100 low U-index ones (20.74% of all buyback events). The distribution of the U-index of all buyback events is shown in Figure 2. Table 1, Panel A, shows the three-factor as well as the five-factor IRATS for high U- index and low U-index firms. The interesting conclusion is that using the five-factor model improves the predictive power of the U-index: high U-index firms earn 4 year excess returns of 23.59% (t=9.41) while low U-index firms only earn 5.95% (t=3.17), hence 17.64% less than the high U-index ones. Starting from 12 months after the announcement, high U-index firms always beat low U-index firms. When we use the three-factor model, we find similar conclusions, but the results are weaker. For example after 48 months the high U-index firms now earn excess returns of 24.21%, which is only 11.66% higher than the low-u-index firms. Note that, consistent with Peyer and Vermaelen (2009) the low U-index buyback stocks earn significant positive excess returns too. It is difficult to find a portfolio of buyback stocks that under-performs in the long run. So the term overvaluation should be interpreted with caution. The Undervaluation Index is a proxy for the likelihood that the buyback is driven by undervaluation. It does not imply that low U-index firms are overvalued. It means that for these firms the buyback is less likely to be driven by undervaluation, but by other reasons such as managing capital structure, avoiding dilution from executive stock options etc. Table 1, Panel B, shows that this conclusion holds when we use the Calendar Time 10

12 method. Regardless of the horizon, high U-index stocks almost always beat low U-index stocks. As in the case of IRATS, the five-factor model improves the selectivity of the Undervaluation Index: low U-index now no longer earn significant excess returns after 48 months. Figure 3 summarizes the IRATS results in more detail by showing the cumulative abnormal returns during the 6 month pre and 48 month post event period, using the five-factor model. Results are shown for the total sample of buybacks and equity issues, as well as for high and low U-index buyback samples Buybacks followed by Equity Issues The results so far show that firms that repurchase shares are good at market timing, in particular the small beaten up value stocks. On the other hand the average equity issuer does not seem to be driven by market timing in general. However, firms that are good at market timing when buying back undervalued stock are perhaps also good at recognizing when their shares are overvalued. Note that successful market timing requires two managerial characteristics: ability to time the market as well as willingness, i.e., accepting the idea that using superior information to benefit long term shareholders at the expense of other shareholders is the right thing to do. During our sample period ( ) 1,085 companies in our data set both announced buybacks and issued equity, but in only 506 cases a company announced a subsequent equity issue within 4 years after the buyback announcement. We now compute the cumulative excess returns for these firms under two scenarios. First, the no exit scenario, where we hold the stock for 48 months after the buyback announcement. Second, the exit scenario, where we sell the shares as soon as the company announces an equity issue. Of the 506 such events, 103 happen within 1 year from the buyback announcement, 261 happen within 2 years and 407 happen within 3 years. Note that this grouping of the events is done with hindsight: it is not possible to know at the time of the buyback announcement whether there will be a subsequent SEO or not. We are simply asking the question whether 11

13 those firms that announced a buyback when they appeared undervalued issued equity when they were overvalued. Figure 4 shows the percentage of repurchasing firms that announced an equity issue within 48 months. The average percentage is 4.9% and there are only 2 years (1989 and 1990) where the percentage is larger than 10%. Table 3 shows that repurchasing firms that issued stock within 48 months after the buyback are remarkable timers. Long-term excess returns after 4 years are 50.24% (t=9.59), more than four times as large as for the overwhelming majority of firms that do not issue stock subsequently. These results are graphically displayed in Figure 5 (Panel A). Repurchases by firms that do not issue equity in the next 48 months are followed by long term excess returns of only 10.84%. One interpretation is that these firms believe they are undervalued but as long as they remain undervalued they do not think it is appropriate to issue stock. The Calendar Method results in Panel B of Table 3 show a relatively large drop of the excess returns over time (e.g., from 1.03% after 12 months to 0.73% after 48 months) indicating potential benefits of exiting a buyback position when there is a subsequent issue. Figure 5 (Panel B) shows the benefits of exiting early. The figure shows a strategy with hindsight where, starting in 1985, we invest in an equally weighted portfolio of only firms that announced a buyback and subsequently issued equity within the 48 months after the buyback announcement. The dashed line shows the cumulative excess return if we sold the stock whenever the firm issued shares within 48 months (the exit strategy). The solid line shows the cumulative excess returns if we sold 48 months after the buyback announcement (the no exit case). The investor who had followed the exit strategy would have earned (after 30 years) a cumulative excess return of 595.3%, significantly larger than the 280.1% of a buy hold for 48 months strategy. Note, however, that because very few firms that buy back stock issue equity within 48 months, a strategy without hindsight where one bought all companies after a buyback and sold only those after a subsequent equity issue would not substantially increase excess returns. Table 4 shows the long run excess returns after the announcement of an equity issue for 12

14 two samples. The first sample (After a Buyback) shows the excess returns for issues for which in the previous 48 months the firm announced a buyback. The second sample (No Prior Buyback) shows the excess returns for all other issue announcements. The fact that excess returns are not significantly different from zero for the post-buyback issuers agrees with the intuition of Figure 5: exiting when there is a subsequent equity issue is the right thing to do for the long-term buyback investor. 4. How robust is the buyback anomaly? The results so far are based on a sample of all buyback and equity announcements over a thirty-year period. As the equity issue anomaly does not survive the Fama and French (2015a) five-factor model, the remainder of the paper focuses on better understanding the buyback anomaly and uses the five-factor model as a benchmark. 6 The purpose of this section is to test the robustness of this anomaly: has it become less important over time because markets have become more efficient? How sensitive is it to the length of the investment period? Could the anomaly be industry-specific? 4.1. Robustness across time periods and investment horizons Table 5 shows excess returns, using both the IRATS and Calendar Time method for different time periods. We consider time periods, which overlap to some extent with past research (Ikenberry, Lakonishok, and Vermaelen 1995, Peyer and Vermaelen 2009, Manconi, Peyer, and Vermaelen 2015 and Fu and Huang 2015): ; ; and The last period was chosen to incorporate the financial crisis and to test whether indeed markets have become more efficient in recent years, or whether managers have been discouraged from market timing by the obvious mistakes that were made by buying back shares before a major financial crisis. 6 All analyses below are also done for equity announcements. However, in agreement with the results in Section 3.1, we find no consistent/robust results for issuers. All issuers results are available upon request. 13

15 Table 5 shows that, regardless of the time period chosen or the method to calculate excess returns, the buyback anomaly remains economically and statistically significant and there is no clear time trend in the data that suggests that markets have become more efficient over time. For example, although the period shows smaller timing ability than the period, excess returns in the period are as large as in period: approximately 16.34% after 4 years using IRATS or 0.49% per month (23.52% after 4 years) when we use the Calendar Time method. There is one exception to the consistency between the IRATS and the Calendar Time results: in the period of , the IRATS method generates excess returns after 48 months of 21.7% (t=10.73) but the Calendar Time method produces statistically insignificant excess returns of 0.19% per month. This result appears to also be inconsistent with Peyer and Vermaelen (2009). However, if one includes the financial sector firms or considers the three-factor model, as Peyer and Vermaelen (2009) do, the calendar method abnormal returns do become significant. 7 Table 6 re-examines whether the U-index of Peyer and Vermaelen (2009) predicts the five factor excess returns for different time periods. The first two columns show the IRATS results and the last two columns show the Calendar Time results. Regardless of the method to compute excess returns, the U-index is an excellent predictor: except for the very short period, buybacks announced by high U-index firms are followed by significantly larger returns than buybacks announced by low U-index firms. There is also no evidence that the U-index is losing its predictive power over time: for example, in the period the difference between high U-index and low index firms (after 48 months, IRATS) was 12.12%, while in the most recent period high U-index firms had 21.61% larger abnormal returns than low U-index firms. 7 Details available upon request. 14

16 4.2. Robustness with respect to estimation of factor betas Note that both event study methods measure alpha (excess return) and betas jointly. In other words, we do not use prior (to investing) information to estimate risk. An investor who wants to exploit the anomaly, however, may want to hedge market (and other) risk and would need to estimate betas using past data. If the buyback signals a change in risk (as argued by Grullon and Michaely (2004)) it is not obvious that such a hedged strategy would work. To further study the robustness of the buyback anomaly, we simulate a portfolio investment strategy starting in The strategy uses past data to estimate the factor betas and measures the abnormal returns of buyback portfolios over different investment horizons. While this is not an accurate measure of the returns of a buyback fund - as we do not consider transaction costs, turnover issues, or other operational issues (see for example Mitchell and Pulvino (2001)) - it provides us with an estimate of what would have happened to an investor who starts investing in 1985 in an equally weighted portfolio of buyback stocks and holds them over various horizons. Specifically, we consider the following trading strategy: construct the first day of every month an equally weighted portfolio of all companies that announced buybacks during the previous N months, for a given holding period of length N (which can be chosen). Thus, once a company makes an announcement, it enters the portfolio on the first day of the following month and remains there for N months. Note that the portfolio is re-balanced (the first day of) each month. This unhedged strategy generates a time series of returns. Each month (when we re-balance the portfolio) we also use the previous 18 monthly returns of this time series to calculate the (portfolio level) time series betas of all five factors. This allows an investor to determine the betas for the factor risks using data available at the time of portfolio formation. We report the returns of such a portfolio strategy for different holding months N = 1, 3, 15

17 6, 12, 24, 36, 48 in Figure 6. 8 The basic conclusion is that the shorter the investment horizon the larger the excess returns. Specifically, at the end of 2014 the cumulative returns from the 1 month, 6 month, 12 month, 24 month, 36 month and 48 month holding periods are respectively equal to 288.3%, 220.5%, 141.1%, 119.4%, 100.6%, 104.4% and 100.2%. This is not surprising as the Calendar Time results in Table 1 show that the monthly excess returns decline when the investment horizon becomes longer. However, Figure 6 allows us to verify that the excess returns are not simply the result of outperformance during a particular time period. Table 9 shows the monthly and yearly returns of this five-factors hedged strategy for N=12. The table shows that in 20 of 30 years the returns are positive, with a large 31.6% excess return in In only one year (2000) the strategy generates an abnormal loss larger than 2.8%. Despite using pre-portfolio formation data to estimate the betas, unlike both the IRATs and Calendar Time methods that use hindsight to estimate risk, the hedged portfolio has very low betas with the five factors. For example for the N = 12 months holding period, the betas for the five factors Market, SMB, HML, RMW, and CMA are respectively 0.007, 0.023, , and The corresponding betas for the unhedged strategy are 1.042, 0.567, 0.201, and This also indicates that the returns shown in Figure 6 and Table 9 are close to excess returns, i.e. returns that have basically eliminated all factors risk. This is also consistent with the hypothesis that the buyback announcement itself does not materially change the risk of the repurchasing firms Robustness across Sectors Figure 7 shows the number of buyback events per industry in our sample. The software and semiconductor industries are the most active repurchasers. They also tend to be the most volatile industries, industries where disagreement about fundamental value is large - as we report later in Table 10. Table 7 shows the IRATS cumulative abnormal returns and 8 Results for other holding periods, as in Figure 6, are available upon request. 16

18 Table 8 the Calendar Time method monthly average abnormal returns when we remove one industry at the time, for the top most frequent buyback industries (those for which there are at least 300 events in our sample). Note from Table 1 that, after 48 months, the cumulative abnormal returns for the whole sample (using IRATS) is 13.02% and the monthly average excess return (Calendar Time) is 0.22%. So the larger the difference between these numbers and the corresponding numbers for the industry indicated in Tables 7 and 8, the larger the excess returns in the industry removed. For example, using IRATS, deleting the software industry lowers the CAR from 13.02% to 9.62%, a 3.4% decline. This is the largest decline in Table 7, indicating that buybacks in the software industry are followed by the largest excess returns. However, deleting Retail, Insurance, Machinery, Meals and especially Chemical stocks improves the excess returns. Of course, these differences could be explained by differences in U-index levels or other indicators of the likelihood of misvaluation, a topic we turn to next. 5. Excess returns and volatility There exists a large literature on volatility and stock returns. One of the most puzzling findings is the fact that total volatility and idiosyncratic volatility are negatively correlated with future abnormal returns, when expected returns are calculated using the 3 factor Fama and French (1993) model (see e.g. Ang et al. (2006) (Table VII)). This volatility anomaly also survives after using the Fama and French (2015a) 5 factor model, at least for small firms, although using profitability factors deflates the abnormal returns Ciliberti, Lemprire, Beveratos, Simon, Laloux, Potters, and Bouchaud (2015). Perhaps the buyback and the volatility anomaly are related: are the buyback firms with the largest excess returns also firms with the smallest (idiosyncratic) risk? Or can we make arguments that the opposite is true, if we accept the fundamental proposition of this paper, i.e. that excess returns are a result of the fact that managers are on average successful in taking advantage of an 17

19 undervalued stock price? 5.1. Idiosyncratic Risk The main theory behind the buyback anomaly is that firms may have superior companyspecific information. Such situations are more likely in industries or companies where the value is driven less by market wide factors, i.e., by highly idiosyncratic companies. So if buybacks are driven by market timing this superior information hypothesis predicts that there should be a positive relation between idiosyncratic returns and volatility. To test this hypothesis, for each event we measure the five-factor regression R 2 using the 6-months daily returns just before the event announcement. 9 We define two types of events: low idiosyncratic (high R 2 ) and high idiosyncratic (low R 2 ) events, depending on whether the five-factor regression R 2 was in the top or bottom 20% of the R 2 of all CRSP companies: each month we use the daily returns of all CRSP stocks for the previous 6 months until the one before last day of the previous month to calculate all companies five-factor regression R 2. We also define the idiosyncratic score of a firm to be the percentile of its 1 R 2 across all CRSP firms that month. Note that we do not need to define 20 breakpoints as Fama-French do, and for simplicity we focus on the two extreme quantiles only. Table 10, columns (1) and (2) show the percentage of high and low idiosyncratic risk events across all industries for which we have at least 100 buyback events in our sample. The healthcare industry has the largest percentage of firms classified as high idiosyncratic, while cyclical industries such as steel, construction and chemicals contain a large number of low idiosyncratic firms. Table 11 shows the IRATS and Calendar Time abnormal returns for high and low idiosyncratic buyback events-companies. Focusing on IRATS, high idiosyncratic buyback stocks earn 23.52% after 48 months, more than three times the excess returns of the low idiosyn- 9 Using shorter time windows, e.g., 1 month, or using the idiosyncratic volatility as in Ang et al. (2006), leads to the same conclusions - results available upon request. However, as we want to differentiate between idiosyncratic companies and high volatility ones, to consider both the effects of company specific information and of the option value of a buyback announcement, we separately study the relations with R 2 and volatility. See also Li, Rajgopal, and Venkatachalam (2014) for a discussion on this issue. 18

20 cratic announcements. The results using the Calendar Time method confirm these findings. Table 11 also tests whether adjusting for idiosyncratic risk improves the predictive power of the U-index. Regardless of the time horizon and the event study method, the U-index works only for idiosyncratic companies. After 48 months, based on the IRATS methods, high U-index high idiosyncratic companies earn 39.68% (t=8.53). Low idiosyncratic high U-index firms have only an insignificant excess return of 5.45% (t=0.76), while for low idiosyncratic firms the low U-index IRATS excess returns are significant (7.95%, t=2.26). Note however that we only have few events in low idiosyncratic, high U-index (303 events) and high idiosyncratic, low U-index (165 events) categories. The Calendar Time results provide the same picture: only for the high idiosyncratic, high U-index firms we obtain significant (t=3.49) monthly excess returns of 0.65%. The high idiosyncratic and low U-index firms have non-significant (t=0.86) monthly excess returns of 0.15%. 10 Figure 8 summarizes our results. It shows the CAR based on IRATS (Panel A for the high U-index firms, B for the low U-index firms, and C for all firms). In agreement with Table 11, the striking result (Panel A) is that the U-index is not a good predictor of excess returns for stocks largely driven by market factors (low idiosyncratic firms). This is strong evidence that excess returns after buybacks are driven by superior company-specific information of the management. The finding that 1 R 2 and idiosyncratic volatility (IVOL in Ang et al. (2006), measured as the standard deviation of the residuals of the factor model regression) are positively related to future excess returns is inconsistent with Ang et al. (2006) who find a negative relation between IVOL and expected returns. However, Stambaugh et al. (2015) argue that the relationship between IVOL and returns becomes positive for undervalued stocks. Their argument is that IVOL represents risk that deters arbitrage and therefore creates mispricing. 10 We also calculated the returns of a hedged strategy similar to Figure 6 (Panel B). Starting in 1985 we form a portfolio of all stocks that announced a buyback during the previous N months and hold the stock for N months. High idiosyncratic companies earn cumulative excess returns of 194.1% (153.1%) for the 12 (48) month holding strategy. These excess returns are higher than the 107.8% (83.5%) of the corresponding low idiosyncratic sample. 19

21 Using a proxy for mispricing based on 11 anomalies they find indeed a positive relation between IVOL and future returns for undervalued stocks. Their most under-priced high IVOL stocks earn monthly excess returns (relative to the Fama-French three-factor model) of 0.56% per month which is quite similar to the 0.41% per month reported in our Table 11 Panel B (using the five-factor model) Volatility The announcement of a buyback program is not a firm commitment, but an option to buy back stock. Ikenberry and Vermaelen (1996) model this flexibility as an exchange option in which the market price of the stock is exchanged for the true value of the stock. They predict that, as with all options, the value increases with the volatility. The intuition is that the larger the volatility, the larger the probability that the market price may deviate from the true value. This enhances the timing ability of the manager-insider. They show that this option can have a lot of value, something that may not be realized at the time of the announcement of the buyback authorization. Hence, perhaps total volatility is a better prediction of excess returns than idiosyncratic volatility or the U-index. Or perhaps volatility can be an additional, next to the U-index and idiosyncratic volatility, indicator of the likelihood that the buyback is driven by undervaluation. For each event we measure their pre-announce returns volatility with the standard deviation of their daily stock returns over the 6 months prior to the buyback announcement. We define two types of events: low volatility and high volatility events, depending on whether volatility was in the top or bottom 20% of the volatilities of all CRSP companies, as we did for R 2 above: each month we use the daily returns of all CRSP stocks for the previous 6 months until the one before last day of the previous month to calculate all companies daily returns volatilities. We also define the volatility score of a firm to be the percentile of its volatility across all CRSP firms that month. Note that, again, we do not need to define 20 breakpoints as Fama-French do, and for simplicity we focus on the two extreme quantiles 20

22 only. In total we have 2,531 high volatility buybacks-events and 2,531 low volatility ones. Table 10, columns (3) and (4) show the percentage of high and low volatility events across all industries for which we have at least 100 buyback events in our sample. Table 12 shows the IRATS and Calendar Time abnormal returns for high and low volatility buybacks events-companies. Focusing on IRATS, high volatility buyback stocks earn 36.92% after 48 months, while low volatility events have non significant abnormal returns for any period. The results using the Calendar Time method confirm these findings. 11 Table 12 also tests whether the U-index is valid for high volatility events, as well as whether adjusting for volatility improves the predictive power of the U-index. Regardless of the time horizon and the event study method, the U-index works for high volatile companies. After 48 months, based on the IRATS methods, high U-index high volatility companies earn 45.61% (t = 9.05). Low U-index high volatility companies earn 31.12% (t = 4.32). The Calendar Time results provide the same picture. Figure 9 summarizes the results for the total sample and the high and low U-index sample. The main difference with Figure 8 is that now also low volatility/high U-index firms earn significant excess returns of 15.3% after 48 months An Enhanced U-index for Buybacks Table 13 shows how the high/low U-index low/high idiosyncratic risk, and low/high volatility buyback events overlap, while Table 14 shows the correlations between the idiosyncratic, volatility, and U-index scores. Overall we see that although high U-index firms tend to have high idiosyncratic risk and high volatility, while high idiosyncratic risk firms tend to also have high volatility, the overlap is not very high. For example from Table 13 we learn that only 27.1% of the high volatility stocks that are classified as having either high 11 We also calculated the returns of a hedged strategy similar to Figure 6 (Panel B). Starting in 1985 we form a portfolio of all stocks that announced a buyback during the previous N months and hold the stock for N months. High volatility companies earn cumulative excess returns of 160.1% (167.9%) for the 12 (48) month holding strategy, which are higher than the 129.1% (103.3%) of the corresponding low volatility sample. 21